System and method for determining orientation based on solar positioning

ABSTRACT

Determination of the orientation of a unit is based on solar positioning. An actual measurement of the position of the sun is taken and compared to a theoretical determination of the position of the sun. By comparing the actual and theoretical positions, the orientation of the unit is determined in an accurate, reliable, and economical manner.

BACKGROUND OF THE INVENTION

In certain applications, it is advantageous for a field-deployed unit tohave knowledge of its orientation. For example, a unit may requireknowledge of its own orientation relative to a target, or an array ofunits may require knowledge of their respective orientations relative toeach other and/or relative to a target. In a data share process, forexample, multiple units communicate with each other in order toeffectively track a target of interest, or in order to determine whichunit can most effectively engage a target. Efficient processing requiresorientation estimates by each unit involved in the tracking process. Inanother function, referred to as control station communication, eachindividual unit communicates with a central computer to provide anoperator of the central computer with updated tracking information sothat the operator can plan an effective solution. Again, in this case,orientation information for each unit involved is critical for accurateengagement.

While the popular global positioning system (GPS) provides an accurateaccounting of latitude, longitude, and altitude of a unit, as well as anaccurate time reference, the orientation of a unit cannot be derivedsolely from the received GPS data. Accordingly, magnetic and electroniccompasses remain as popular mechanisms for providing orientationinformation. When properly calibrated, such compasses commonly achieveorientation readings to within a tolerance of ±2°.

A magnetic compass detects the horizontal direction of the earth'smagnetic field. Using this reference, a unit can derive its orientation.However, the accuracy of a magnetic compass is limited by environmentalissues, such as hard and soft iron effects in the surrounding landscape,and variations in the earth's magnetic field. In addition, the magneticfields generated by nearby system electronics can further interfere withaccurate readings. Furthermore, a magnetic compass requires periodiccalibration, which can be an expensive operation when the unit is inlong-term storage or when the unit is deployed in the field.

The electronic compass compensates for the hard and soft iron effects byusing specific calibration algorithms. Soft iron effect calibration isquite complicated and requires an initial calibration procedure when aunit is deployed in the field. The initial calibration can be easilydisturbed if the unit is moved, and a complete system recalibration isrequired every few months. Such recalibration is often times impracticalor impossible for field-deployed units. Furthermore, electroniccompasses are sensitive to temperature, especially outside the range of−40 C. to 80 C.

SUMMARY OF THE INVENTION

The present invention is directed to a system and method for determiningthe orientation of an object based on its positioning relative to asource of electromagnetic energy, for example, the sun. In this manner,the present invention provides an accurate, reliable, and economicalapproach for determining object orientation, without being subject tothe limitations associated with the conventional electronic and magneticcompasses.

In one aspect, the present invention is directed to a system fordetermining the orientation of an object relative to a source ofelectromagnetic radiation. The system includes a plurality of sensors,each of the sensors producing a corresponding output signal when placedin the path of electromagnetic radiation emitted by a source. Acontroller receives the output signals of the sensors, and fordetermining the orientation of the object relative to the source basedon the sensor output signals.

The source of the electromagnetic radiation may comprise, for example, aheavenly body, for example, the sun. The electromagnetic radiation isfor example, of a type selected from the group consisting of visibleradiation, infrared radiation, and ultraviolet radiation.

In one example, the sensors are optical sensors, for examplephotodiodes. The output signals are derived from the intensity of lightradiation received at the photodiodes. Each of the sensors has acorresponding viewing angle having a center line, and the center linesare at known orientations relative to each other. The center lines may,for example, lie on a plane and/or may intersect at a common point.

In another example, the controller samples multiple sets of the sensoroutput signals at periodic time intervals. In this case, thecontroller's determination of the orientation of the object is based onmultiple sets of the sensor output signals. The controller furtherdetermines a subset of the output signals of the sensors, for example atleast three sensor output signals, having signal levels that are greaterthan those of the other output signals, and fits a polynomial to theoutput signals of the subset. The controller then determines one of amaximum and minimum of the polynomial, and determines the orientation ofthe object based on the one of the maximum and minimum.

The controller optionally determines the orientation of the objectfurther based on a known factor of the type consisting of: time,latitude, longitude, and altitude.

The controller determines the orientation of the object further based ona theoretical determination of the electromagnetic radiation sourceposition. The controller further determines the orientation of theobject by comparing the theoretical determination of the electromagneticradiation source position to an actual determination of the positionbased on the sensor output signals.

In another aspect, the present invention is directed to a system fordetermining the orientation of an object relative to a source ofelectromagnetic radiation. The system includes a two-dimensional arrayof sensors, each of the sensors in the array producing a correspondingoutput signal when placed in the path of electromagnetic radiationemitted by a source. A lens directs the electromagnetic radiation fromthe source onto the two-dimensional array. A controller receives theoutput signals of the sensors, and determines the orientation of theobject relative to the source based on the sensor output signals.

The two-dimensional array of sensors comprises, for example, acharge-coupled device (CCD) array, or a bolometer array.

The output signals of the sensors may comprise binary signals thatindicate those sensor elements of the two-dimensional sensor array thatare activated in response to receiving the electromagnetic energy at alevel above a predetermined threshold. The controller determines theorientation of the object based on multiple samples of the sensor outputsignals taken at predetermined time intervals. The controller furthertracks elements of the sensor array that are activated at each sampleinterval, and fits a polynomial to the activated sensor elements overtime. The orientation of the object is then determined based on thepolynomial.

The lens may comprise, for example, a pinhole in a housing bodycontaining the two-dimensional array of sensors.

In another aspect, the present invention is directed to a method fordetermining the orientation of an object relative to a source ofelectromagnetic radiation. Electromagnetic radiation emitted by a sourceis received at a plurality of sensors. Each of the sensors produces acorresponding output signal in response to the received electromagneticradiation. An actual position of the source of electromagnetic energy isdetermined based on the sensor output signals. A theoretical position ofthe source of electromagnetic energy is computed and compared with theactual position to determine the orientation of the object.

By comparing the actual and theoretical positions, the orientation ofthe unit is determined in an accurate, reliable, and economical manner.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, features and advantages of theinvention will be apparent from the more particular description ofpreferred embodiments of the invention, as illustrated in theaccompanying drawings in which like reference characters refer to thesame parts throughout the different views. The drawings are notnecessarily to scale, emphasis instead being placed upon illustratingthe principles of the invention.

FIG. 1 is a top view of a first embodiment of an apparatus fordetermining the orientation of an object, in accordance with the presentinvention.

FIG. 2 is a schematic diagram of the embodiment of FIG. 1, in accordancewith the present invention.

FIG. 3 is a conceptual view of the embodiment of FIG. 1 deployed in afield environment, in accordance with the present invention.

FIG. 4 is top view of the deployed embodiment of FIG. 3, in accordancewith the present invention.

FIGS. 5A, 5B, 5C, and 5D are top conceptual views of various alternativeconfigurations of the embodiment of FIG. 1, in accordance with thepresent invention.

FIG. 6 is a perspective view of an apparatus for determining theorientation of a unit in accordance with a second embodiment of thepresent invention.

FIG. 7 is a conceptual illustration of the embodiment of FIG. 6 deployedin a field environment, in accordance with the present invention.

FIG. 8 is a top view of the CCD array of the embodiment of FIG. 7, inaccordance with the present invention.

FIG. 9 is a chart illustrating a curve generated from the excited pixelsof the CCD array of FIG. 8, in accordance with the present invention.

FIG. 10 is a top view of the projection of the position of the sun ontoa two-dimensional array of sensors, assuming the sensor array to bemounted level with respect to the ground, in accordance with the presentinvention.

FIG. 11 is a top view of the projection of the position of the sun ontoa tilted two-dimensional array of sensors, comparing the level-mountedarray of FIG. 10 with a tilted array, in accordance with the presentinvention.

FIG. 12 is a side view of the projection of FIG. 11, in accordance withthe present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The system and method of the present invention provide for the abilityto determine the orientation of an object based on solar positioning. Inone embodiment, a plurality of sensors are housed in a unit that isstationary for an extended period of time. The sensors sampleelectromagnetic energy, for example visible, infrared, or ultravioletradiation, received from the sun, or other heavenly body or energysource, at predetermined time intervals. The time intervals arepreferably long enough such that the earth's rotation relative to thesun is discernable, and in this manner, the sensor readings at thepredetermined time intervals track the motion of the sun in the skyrelative to the unit. For example, the time intervals may comprise 10-30minute intervals. In this manner, assuming the latitude and longitude ofthe unit are accurately known, as well as the time, then the orientationof the unit can be accurately determined.

The energy emitted by the sun is intensive enough such that it can bereadily detected without the need for distinguishing it from other lightsources. In addition, the sun has a relatively small angular radius, sothat it can be modeled as a point source, which simplifies relatedcalculations. The position of the sun with respect to the earth at anytime can be predicted using a three-dimensional polar axis with thecoordinates of position, altitude angle, and azimuth angle. The positionis measured in degrees latitude and degrees longitude; data that can beaccurately and economically obtained from a GPS receiver. The solaraltitude angle (α) is defined as the angle between the sun and thehorizontal plane of sight. The solar azimuth angle (Y) is defined as theprojection of the sun onto the horizontal plane of sight. A table ofdefinitions and parameters, as well as formulae, related to thecalculation of the sun's position relative to a location on earth aregiven below, as cited in Nuwayhid, R. Y., Mrad, F., and Abu-Said, R.,“The Realization of a Simple Solar Tracking Concentrator for UniversityResearch Applications,” Renewable Energy, vol. 24, no.2, pp. 207-222,October 2001:

-   -   L Latitude of the location—the angle between a line from earth's        center to the location and its projection on the equator plane.    -   Lloc Longitude of the location.    -   α Solar altitude—the angle between the sunray and the horizontal        plane of sight.    -   n Day of the year.    -   δ declination—angular position of the sun at solar noon with        respect to the plane of the equator.    -   ω Hour angle—the angular displacement of the sun east to west of        the local meridian due to the rotation of the earth.    -   Ys Solar azimuth—the deviation of the projection of the sunrays        on the horizontal surface and the local meridian.    -   Zenith The point directly upwards—a perpendicular line to a        point in the sky from the horizontal plane at the location    -   θ Angle of incidence—angle between the projection of the normal        to the concentrate plane to the horizontal and local meridian.    -   β Angle between the surface and the horizontal.

The first step in calculating the solar altitude and azimuth angles isto determine the solar time, which describes the time of the sun withrespect to the local time.Solar Time=standard time+(Lst−Lloc)/15+E   (1)where E=9.87 sin 2B−7.53 cos B−1.5 sin B   (2)and B=360(n−81)/364   (3)

The general relationship of the angles defined above is as follows:cos θ=sin δ sin L cos β−sin δ cos L sin β cos Y+cos δ cos L cos δ cosω+cos δ sin L sin β cos Y cos ω+cos δ sin β sin Y sin ω  (4)

The incident angle θ can be determined according to the followingrelationship:cos θ=cos α cos β−sin α sin β cos (Ys−Y)   (5)where δ=sin (360(284+n)/365))   (6)

Finally, the exact solar altitude and azimuth angles can be calculatedto obtain the trajectory of the sun according to the followingrelationship:sin α=sin L sin δ+cos L cos ω cos θand sin Y=cos δ sin ω/cos α  (7)

The above equations demonstrate that it is always possible to determinethe trajectory of the sun in terms of its altitude and azimuth angles α,Y. Derivation of these values require knowledge of the standard time aswell as the latitude and longitude position of the unit. An on-board GPSsystem is suitable for retrieving this data, which can be provided to acontroller that processes the above formulae using an algorithm todetermine the position of the sun.

In a first embodiment, as shown in FIG. 1, a plurality of sensors, forexample optical sensors in the form of photodiodes D1 . . . D8, aremounted in a housing 20 at a known angle 28 relative to each other, forexample, 45°. The diodes themselves preferably have a fairly narrowviewing angle λ, for example on the order of 5-10°, and are preferablyrecessed into slots 24 formed in the housing body 20 to further limitthe viewing angle λ. In this manner, the photodiodes D1 . . . D8 tend toreceive only that electromagnetic energy which is oriented within therespective viewing angles. A reference point, or axis R1, can beselected as a frame of reference for the unit. For example referenceaxis R1 can be selected as a radial axis that intersects the center ofthe unit and the first diode D1. Rotation angle, or orientation, is thusdetermined relative to this reference axis R1.

Other suitable sensors include, but are not limited to,phototransistors, avalanche photodiodes, microchannel plates, andphotoresistors. P-i-n and Schottky-barrier photodiodes may also be used.

The viewing angles λ of the diodes D1 . . . D8 each have a center line25, and in a preferred embodiment, the center lines 25 of the diodeviewing angles λ lie on a plane and intersect at a common point. In analternative embodiment, the diodes D1 . . . D8 may be slightly tilted inthe housing 20 in an upward direction, so as to increase exposure to thesun when the sun is at a higher elevation.

The diodes D1 . . . D8 each generate an independent output signal 26,for example, in the form of a voltage or a current that is provided to acontroller 22. The controller 22 samples the output signals 26 atregular intervals, for example at 15 minute intervals. However, undercertain circumstances, a single reading may be sufficient fordetermining the orientation. In one embodiment, the controller 22determines the output signals that indicate the three highest intensitymeasurements of the sampled diodes D1 . . . D8. The controller 22 fits apolynomial to the three intensity measurements at each sample intervaland determines the maximum of the polynomial. The maximum provides theposition of the sun relative to the unit in terms of the sun's azimuth.

The polynomial curve fitting process determines where the peak solarintensity is located relative to the known diode (or photodetectors)locations, and hence determines the position of the sun. A polynomial isderived that closely matches or ‘fits’ the three highest intensitiesdetected by the photodetectors. The order of the polynomial is arbitraryand may be set prior to receiving any actual intensity levels. Forexample, a processor implementing the curve fitting may be programmed tofit a fifth-order polynomial, e.g., ax⁵+bx⁴+cx³+dx²+ex+f=y, to thedetected intensity values, where y-values are intensities, and the knownx-values are three of the detector locations. Once a curve or polynomialis “fit” or calculated, a maximum (extreme) is determined bydifferentiating the polynomial. The first derivative with respect to xof the polynomial gives the slope of the polynomial and will locatepoint of zero-slope. A second derivative determines the concavity of anyextrema (e.g., maxima or minima), with a positive concavity indicating alocal minimum, and a negative concavity indicating a local maximum. Theposition of the local maximum is the point where the solar intensity isthe greatest and where the sun should be located. The x-position of thislocation may be translated to a polar bearing relative to the centerlines of the photodetectors. This bearing is the bearing of the sunrelative to the sensors and the unit on which they are mounted. Byknowing from astronomical tables which direction the sun is located, byknowing the position on earth (latitude and longitude) where the unitis, and by knowing the time of day, the position indicated by the curvefitting is compared to the known, expected position of the sun. In thismanner the orientation of the unit may be determined.

In determining the expected position of the sun, the following formulae,as discussed in Cornwall, C., “General Solar Position Calculations,”Mar. 21, 2003, available online athttp://www.srrb.noaa.gov/highlights/sunrise/solareqns.PDF; andBlanco-Muriel, M., “Computing the Solar Vector,” Solar Energy, vol. 70,no. 5, pp. 431-441, 2001, may be implemented in a software programoperating on the microcontroller:Fractional Year=γ=2π/365(day_of_year−1+(hour−12)/24)   (8)Equation of time=eqtime=229.18(0.000075+0.001868 cos γ−0.032077 sinγ−0.014615 cos 2γ−0.040849 sin 2γ)   (9)Declination angle=decl=0.006918−0.399912 cos γ+0.070257 sin γ−0.006758cos 2γ+0.000907 sin 2γ−0.002697 cos 3γ+0.00148 sub 3γ  (10)Time offset=time₁₃offset=eqtime−4*longitude+60*timezone   (11)where longitude is in degrees and timezone represents hours from UTC.True solar time=tst=hr*60+mn+sc/60+time_offset   (12)where hr=0-23, mn=0-60, and sc=0-60.Hour angle=ha=(tst/4)−180   (13)Zenith angle=φ: cos φ=sin(lat)sin(decl)+cos(lat)cos(decl)cos(ha)   (14)Azimuth angle=θ: cos(180−θ)=(sin(lat)cos φ−sin(decl))/(cos(lat)sin φ)  (15)

In this manner, the theoretical location of the sun is determined as afunction of known time, latitude and longitude.

The curve fitting process, for determining the actual position of thesun with respect to the unit, may be implemented by least-squaresalgorithms, i.e., ones that minimize the square of error between actualvalues and a trial polynomial. Such algorithms, as well as the aboveformulae for determining the theoretical position of the sun, can beimplemented for example as C++, C, MATLAB, and assembly language.Suitable hardware such as digital signal processors (DSPs), applicationspecific integrated circuits (ASICs), and central processing units(CPUs) may be used to run such algorithms and processes.

Upon determination of the actual position of the sun relative to theunit based on the processing of the sensor data, and upon determinationof the theoretically expected position of the sun based on the knownlatitude, longitude, and time data, the actual sun position and theexpected sun position are compared to determine the orientation of theunit.

For example, with reference to FIG. 1, if the theoretically expectedposition of the sun is determined to be at an azimuth of 90° (i.e., dueeast), and the unit determines that the sun's position is at a certainposition between two diodes of the unit (e.g., ⅖ths between diodes D7and D8, then the orientation of the reference line, for examplereference line R1, of the unit is determined to be at 153°.

Assuming a fully calibrated system, a single measurement, that is asingle sample, may be sufficient to provide the orientationdetermination. This is particularly true when the sun is low on thehorizon. However, assuming an uncalibrated system, several measurementscan be taken periodically over time to provide a series of simultaneousequations that can solve for the unknown in the responsivity ordetectivity of the diodes.

Linear algebra techniques may be used to solve for “N” unknownquantities by having “N” linearly independent equations. The unknownquantities here, in an uncalibrated embodiment, may include a certainnumber of variations of detectivity (responsivity) between nominallyidentical photodetectors and variations in alignment of thephotodetctors (deviations from designed orientation). The hardware andsoftware platforms described above are suitable for solving suchsimultaneous equations.

FIG. 2 is a detailed schematic drawing of the embodiment of FIG. 1. Eachdiode circuit 38 comprises a photodiode Dn in the form of aphototransistor that operates as a photodiode when configured as shown.The cathode of each photodiode Dn is coupled to a power source, and theanode of each is coupled to a parallel resistor Rn-capacitor Cncombination that is in turn coupled to ground. The photodiodes operateas a current source that is proportional to the amount of lightreceived. Therefore, the light intensity can readily be measured byconnecting the photodiode to a resistor Rn in parallel. For example 100kohm resistors can be used to obtain measurements in the range of 0 to 4volts. A 0.1 μF capacitor Cn is connected in parallel with each resistorRn to obtain accurate measurements. Such photodetector devices aretypically designed so that a particular n-doped or p-doped material usedin the p-n junction of the diode will absorb the incident light. This isdone by selecting the active material based on its bandgap energy and byknowing the particular frequency of light at which detection is desired.The part (anode, cathode, n-side, p-side) that is desired to absorb thelight has a lower bandgap energy than the other part(s), which will havea higher bandgap energy and which will be transparent to the light ofinterest.

The anode of each photodiode Dn provides an output signal 26 that istransmitted to controller 22. Controller 22 may take the form of ahard-wired circuit, or preferably a microcomputer or mixed-signalmicrocontroller, such as the MSP430F149, available from TexasInstruments, Inc., Dallas, Tex., which has a 12-bit analog-to-digitalconverter and is capable of performing the data sampling, polynomialfit, theoretical sun positioning and other related calculations fordetermining the orientation of the unit. The controller 22 also receivesGPS information, including latitude, longitude, and, if desired,altitude information, as well as time information from the GPS receiver23.

FIG. 3 is a perspective view of the photodiode-based embodiment of FIG.1 mounted to a unit 30 that is deployed in the field. The sun 32 isillustrated at first, second, and third positions, 32A, 32B, 32Ccorresponding three periodic sample times. At the first sample time, theposition of the sun 32A relative to the unit 30 is such that theelectromagnetic energy beam emitted by the sun 33A is at a first anglerelative to the unit 30. Similarly, the energy beams 33B, 33C emitted atthe second and third sampling times are at different angles relative tothe unit 30, as a result of the earth's rotation between the sample timeincrements.

As shown at the top view of FIG. 4, the three respective energy beams,33A, 33B, 33C are incident on the housing 20 at slightly differentangles, and therefore the intensity level received by each of the diodesfacing that direction, for example diodes D6, D7, D8 and D1, aredifferent for each sample period. For example, diode D7 would have arelatively strong intensity reading from beam 33A and a relatively weakreading from beam 33C. Diode D6 would have a relatively weak intensityreading from beam 33A, and weaker readings from beams 33B and 33C. Ateach sample time, based on the detected difference in intensity level, acomputer or microcontroller, for example controller 22, with accurateknowledge of the time, and latitude and longitude of the deployed unit,accurately computes the orientation of the deployed unit, as describedabove. Through the use of multiple samples, as shown, variability inenvironmental exposure, for example due to cloud cover, sensorresponsivity, and sensor placement can be resolved by themicrocontroller of the unit 30, as the additional samples provideadditional data points, for greater accuracy.

Although the photodiodes D1 . . . D8 of the embodiment of FIG. 1 arearranged generally on a circle, or octagon, having viewing angle centeraxes that lie at 45° relative to each other, other geometricarrangements apply equally well to the principles of the presentinvention and are therefore equally applicable. For example, in FIG. 5A,eight diodes D1 . . . D8 are arranged on a square configuration, theviewing angles of the respective diodes D1 . . . D8 being arranged in45° increments, as in FIG. 1. In FIG. 5B, six diodes D1 . . . D6 arearranged in a semicircle configuration, for example at orientations of36° relative to each other. In this example, it is preferable that theunit is deployed such that the diodes D1 . . . D6 are positioned to beexposed to either the sunrise, or sunset, assuming the relative locationof sunrise or sunset to be known to the individual deploying the unit.In the example of FIG. 5C, six diodes D1 . . . D6 are arranged on ahexagon, for example having viewing angles that are oriented 60°relative to each other. FIG. 5D illustrates four diodes D1 . . . D4arranged according to a semicircle quadrant, for example having viewingangles of 30° relative to each other. Again, in this example, it ispreferred that the unit is deployed to be exposed to either the sunriseor the sunset, since the diode viewing angles are limited to one side ofthe enclosure.

FIG. 6 is a perspective view of a second embodiment of the presentinvention that employs a two-dimensional array of diodes, for example acharge-coupled device (CCD) array of sensor pixels that sense lightenergy, or alternatively, for example, a bolometer array of sensorpixels that sense heat energy. The illustrated embodiment includes ahousing 40 that encloses a CCD array 44 coupled to a controller 46. Thecontroller preferably comprises a microcomputer, as described above. Thehousing 40 includes an optical translation unit, for example in the formof a pinhole 42 or lens, capable of focusing a beam of electromagneticenergy incident upon the housing 40 onto the array 44, such that theposition of the energy source relative to the lens 42 is mapped onto thetwo dimensional array 44.

FIG. 7 is a perspective view of the apparatus of the second embodimentof the present invention mounted in a field-deployed unit 48. As the sun32 progresses across the sky (i.e., as the earth rotates relative to thesun) with the passage of time, samples are taken by the CCD array 44 atpredetermined time intervals, for example, at 15 minute intervals. Forexample, at the time of the first sample, the sun 32A emits a beam ofelectromagnetic energy 33A that is directed at a particular angle towardthe pinhole 42 of the housing 40. This energy beam 33A is in turndirected by the pinhole 42 to a corresponding pixel, or a group ofpixels 50 of the CCD array 44, where a primary amount of the energy isdirected. The controller takes second and third samples of the CCD array44 following a predetermined interval of time, such that at each sample,the sun has moved in the sky by a discernable amount to later positions32B, 32C respectively. Therefore, the electromagnetic energy beams 33B,33C emitted at these times are incident on the pinhole 42 of the housing40 at angles that are slightly different of those of the original beam33A. As a result, the beams are redirected by the pinhole to a differentpixel or group of pixels of the array 44 than at the first sample time.In this manner, the movement of the sun 32 relative to the deployed unit48 is mapped onto the pixels of the CCD array 40.

An example of such mapping is shown in FIG. 8, which is a top view ofthe CCD array 44 of the deployed unit 48 of FIG. 7. In this example, itcan be seen that pixel 50A is stimulated during a first sampling, pixel50B is stimulated during a second sampling, and pixel 50C is stimulatedduring a third sampling.

As shown in FIG. 9, the stimulated pixels of the CCD array 44 aretracked by the controller 46 and a curve 52 is approximated based on thestimulated pixels. Based on the approximated curve 52, an accurateaccounting of the time of each sample, and the latitude, longitude, andaltitude of the deployed unit 48, an accurate representation of theorientation of the deployed unit 48 can be determined.

An analogous situation is the movement of the sun and the sun's shadowproduced by a sundial. The pinhole 42 operates as a lens, and the lenshas a focal length. The CCD array 44 is positioned at the focal lengthof the pinhole 42. The image of the sun at each instant in time isfocused on one or a few pixels. While the pixels could be digital(on-off), they could also be analog, or gray-scale. The path of the suncan be determined by the pixel reading and by the knowledge of theimage-reversal (Fourier transform effect) of the lens. This measuredpath is correlated to the expected, known path and position informationof the sun, as provided above. Other lenses, for example optical lensesformed of glass, plastic, sapphire, are equally applicable, assumingthey are transparent at the desired frequency.

The CCD array embodiment further allows for the determination oforientation of a unit when the array device, for example the arraydevice of FIG. 6, is tilted by an unknown magnitude and in an unknowndirection. The solution is most readily understood by first consideringthe solution for the case where the array is mounted level with respectto the ground. Based on the GPS data, the current time and position ofthe host unit are known. From this information, the current azimuth andelevation of the sun are determined, as described above. This azimuthangle is determined, for example, relative to north, from data that mayoptionally be stored in a “look-up” table.

Referring to FIG. 10, assuming the Y-axis 60 of the array 44 to bealigned with the north, then the center of the solar image maps to pointP1, referred to herein as “zero rotation position”. However, assumingthe Y-axis 60 is not aligned with the north, then the actual projectionof the position of the sun on the array will lie along some point on acircle 62. Assuming the actual measured position to be at point P2 onthe array, then the Y-axis of the CCD array is determined to be rotatedwith respect to north by the angle a. Hence, assuming the array to beinstalled in a level position, the orientation of the unit can beresolved with a single measurement.

In a more general case, the CCD array 44 is assumed to be mounted at anangle relative to ground, in other words, the array is “tilted”. In thisexample, the possible set of positions for the projection of the sunonto the array 44 lies along an ellipse 64 as shown in FIG. 11. The tiltand orientation of the array 44 in this example are defined by arotation angle b, and a depression angle c that result in theprojections lying along the ellipse 64. Assuming the x, y coordinatesystem to be oriented such that the Y-axis is aligned with north, thenthe x′, y′ coordinate system shown in FIG. 11 is rotated relative to thex, y coordinate system by an amount of rotation angle b. Assuming thatthe sun's position were to map to point (x_(c),y_(c)) for a level CCDarray, then, assuming the array 44 to be tilted, the sun's positionwould map to a point along the ellipse 64, for example at point(x_(e),y_(e)). In this example, the subscripts “c” and “e” refer to“circle” and “ellipse”.

FIG. 12 is a side view of the mapping of the projected position from thecircle to the ellipse in the x′,y′ coordinate system. The CCD array 44A,44B is shown rotated about the system lens. The angle c represents thetilt depression angle of the tilted CCD array 44B, which is initiallyunknown. The angle d represents the elevation angle of the sun, which isknown. The distance L represents the focal length of the systemoriginating at a point of focus 66, which is also known.

Assuming the above:x′ _(e) =L·tan(c+d)   (16)x′ _(c) =L·tan(d)x′ _(c) =x′ _(e)·tan(d)/tan(c+d)y′_(c)=y′_(e)and:x′ _(e) =L·tan(c+d)   (17)x′ _(c) =L·tan(d)x′ _(e) =x′ _(c)·tan(c+d)/tan(d)y′_(e)=y′_(c)

The transformation from the x,y coordinate system to the x′,y′coordinate system is given by:x′=x·cos(b)+y·sin(b)   (18)y′=y·cos(b)−x·sin(b)x _(e) ′=x _(e)·cos(b)+y _(e)·sin(b)   (19)y _(e) ′=y _(e)·cos(b)−x _(e)·sin(b)x′ _(c)·tan(c+d)/tan(d)=x _(e)·cos(b)+y _(e)·sin(b)   (20)x′ _(c)=tan(d)·(x _(e)·cos(b)+y _(e)·sin(b))/tan(c+d)y′ _(c) =y _(e)·cos(b)−x _(e)·sin(b)Finally, the rotation back to the x,y coordinate frame is given byX _(c) =x _(c)′·cos(b)−y _(c)′·sin(b)   (21)Y _(c) =y _(c)′·cos(b)+x _(c)′·sin(b)The angle “d” is the elevation angle of the sun, which is known.tan(c+d)=(sin(c)·cos(d)+cos(c)·sin(d))/(cos(c)·cos(d)−sin(c)·sin(d))  (22)assuming c1=cos(c), thensin(c)=(1−c1²)^(1/2)   (23)assuming c2=cos(b), thensin(b)=(1−c2²)^(1/2)   (24)

Hence, the point x_(c), y_(c) can be computed from the measuredcoordinate x_(e), y_(e) by solving for the two unknown coefficients c1and c2. With two position measurements, x_(e1), y_(e1) and x_(e2),y_(e2), the coefficients c1 and c2 can be uniquely solved since thepositions x_(c1), y_(c1) and x_(c2), y_(c2) are known from known Solarazimuth and elevation data.

Since the relationships are nonlinear, an iterative search techniquewould need to be implemented, for example in the microcontroller, tosolve for c1 and c2. After solving for c1 and c2 the “tilt” factor ofthe array is eliminated from the measurement and the orientation isresolved in the same manner as in the case of the level CCD array.

The sun's bearing is immediately known when it is on the horizon. Forthis reason, a single sample reading at these times will provide anaccurate determination of orientation. At mid-day a two-dimensionaltrack of the sun's path using the CCD array can help to improve theaccuracy of the measurement. This is especially helpful at lowlatitudes, where at mid-day, the intensities of adjacent photodetectors'would be nearly equal.

While this invention has been particularly shown and described withreferences to preferred embodiments thereof, it will be understood bythose skilled in the art that various changes in form and details may bemade herein without departing from the spirit and scope of the inventionas defined by the appended claims.

For example, while the above example describes preferred sources of theelectromagnetic energy as being heavenly bodies, for example, the sun,the moon, and stars, manmade sources of electromagnetic energy areconsistent with the principles of the present invention, includingsatellites, laser energy (both space-based and earthbound), and thelike, and are therefore equally applicable.

1. A system for determining the orientation of an object relative to asource of electromagnetic radiation comprising: a plurality of sensors,each of the sensors producing a corresponding output signal when placedin the path of electromagnetic radiation emitted by a source; and acontroller for receiving the output signals of the sensors, and fordetermining the orientation of the object relative to the source basedon the sensor output signals.
 2. The system of claim 1 wherein thesource of the electromagnetic radiation is the sun.
 3. The system ofclaim 1 wherein the electromagnetic radiation is of a type selected fromthe group consisting of visible radiation, infrared radiation, andultraviolet radiation.
 4. The system of claim 1 wherein the sensors areoptical sensors.
 5. The system of claim 4 wherein the optical sensorscomprise photodiodes.
 6. The system of claim 5 wherein the outputsignals are derived from the intensity of light radiation received atthe photodiodes.
 7. The system of claim 1 wherein each of the sensorshas a corresponding viewing angle having a center line, and wherein thecenter lines are at known orientations relative to each other.
 8. Thesystem of claim 1 wherein the center lines of the respective sensors areat angles relative to each other.
 9. The system of claim 8 wherein thecenter lines lie on a plane.
 10. The system of claim 8 wherein thecenter lines intersect at a common point.
 11. The system of claim 1wherein the controller samples multiple sets of the sensor outputsignals at periodic time intervals.
 12. The system of claim 11 whereindetermining the orientation of the object is based on multiple sets ofthe sensor output signals.
 13. The system of claim 1 wherein thecontroller further: determines a subset of the output signals of thesensors having signal levels that are greater than those of other outputsignals; fits a polynomial to the output signals of the subset;determines one of a maximum and minimum of the polynomial; anddetermines the orientation of the object based on the one of the maximumand minimum.
 14. The system of claim 13 wherein the subset includes atleast three of the sensor output signals.
 15. The system of claim 1wherein the controller determines the orientation of the object furtherbased on a known factor of the type of a type selected from the typesconsisting of: time, latitude, longitude, and altitude.
 16. The systemof claim 1 wherein the controller determines the orientation of theobject further based on a theoretical determination of theelectromagnetic radiation source position.
 17. The system of claim 16wherein the controller further determines the orientation of the objectby comparing the theoretical determination of the electromagneticradiation source position to an actual determination of the positionbased on the sensor output signals.
 18. A system for determining theorientation of an object relative to a source of electromagneticradiation comprising: a two-dimensional array of sensors, each of thesensors producing a corresponding output signal when placed in the pathof electromagnetic radiation emitted by a source; a lens for directingthe electromagnetic radiation from the source onto the two-dimensionalarray; and a controller for receiving the output signals of the sensors,and for determining the orientation of the object relative to the sourcebased on the sensor output signals.
 19. The system of claim 18 whereinthe two-dimensional array of sensors comprises a charge-coupled device(CCD) array.
 20. The system of claim 18 wherein the two-dimensionalarray of sensors comprises a bolometer array.
 21. The system of claim 18wherein the source of the electromagnetic radiation is the sun.
 22. Thesystem of claim 18 wherein the electromagnetic radiation is of a typeselected from the group consisting of visible radiation, infraredradiation, and ultraviolet radiation.
 23. The system of claim 18 whereinthe sensors are optical sensors.
 24. The system of claim 23 wherein theoptical sensors comprise photodiodes.
 25. The system of claim 24 whereinthe output signals are derived from the intensity of light radiationreceived at the photodiodes.
 26. The system of claim 18 wherein theoutput signals of the sensors are binary signals that indicate thosesensor elements of the two-dimensional sensor array that are activatedin response to receiving the electromagnetic energy at a level above apredetermined threshold.
 27. The system of claim 26 wherein thecontroller determines the orientation of the object based on multiplesamples of the sensor output signals taken at predetermined timeintervals.
 28. The system of claim 27 wherein the controller further:tracks elements of the sensor array that are activated at each sampleinterval; fits a polynomial to the activated sensor elements over time;determines the orientation of the object based on the polynomial. 29.The system of claim 18 wherein the controller determines the orientationof the object further based on a known factor of a type selected fromthe types consisting of: time, latitude, longitude, and altitude. 30.The system of claim 18 wherein the lens comprises a pinhole in a housingbody containing the two-dimensional array of sensors.
 31. The system ofclaim 18 wherein the controller determines the orientation of the objectfurther based on a theoretical determination of the electromagneticradiation source position.
 32. The system of claim 16 wherein thecontroller further determines the orientation of the object by comparingthe theoretical determination of the electromagnetic radiation sourceposition to an actual determination of the position based on the sensoroutput signals.
 33. A method for determining the orientation of anobject relative to a source of electromagnetic radiation comprising:receiving, at a plurality of sensors, electromagnetic radiation emittedby a source, each of the sensors producing a corresponding output signalin response to the received electromagnetic radiation; determining anactual position of the source of electromagnetic energy based on thesensor output signals; computing a theoretical position of the source ofelectromagnetic energy; and comparing the actual position to thetheoretical position to determine the orientation of the object.
 34. Themethod of claim 33 wherein the source of the electromagnetic radiationis the sun.
 35. The method of claim 33 wherein the electromagneticradiation is of a type selected from the group consisting of visibleradiation, infrared radiation, and ultraviolet radiation.
 36. The methodof claim 33 wherein the sensors are optical sensors.
 37. The method ofclaim 36 wherein the optical sensors comprise photodiodes.
 38. Themethod of claim 37 wherein the output signals are derived from theintensity of light radiation received at the photodiodes.
 39. The methodof claim 33 wherein each of the sensors has a corresponding viewingangle having a center line, and wherein the center lines are at knownorientations relative to each other.
 40. The method of claim 33 whereinthe center lines of the respective sensors are at angles relative toeach other.
 41. The method of claim 40 wherein the center lines lie on aplane.
 42. The method of claim 41 wherein the center lines intersect ata common point.
 43. The method of claim 33 further comprising samplingmultiple sets of the sensor output signals at periodic time intervals.44. The method of claim 33 wherein determining the actual position ofthe source of electromagnetic energy is based on multiple sets of thesensor output signals.
 45. The method of claim 33 further comprising:determining a subset of the output signals of the sensors having signallevels that are greater than those of other output signals; fitting apolynomial to the output signals of the subset; determining one of amaximum and minimum of the polynomial; and determining the actualposition of the source of electromagnetic energy based on the one of themaximum and minimum.
 46. The method of claim 45 wherein the subsetincludes at least three of the sensor output signals.
 47. The method ofclaim 33 wherein computing a theoretical position of the source ofelectromagnetic energy is based on a known factor selected from thetypes consisting of: time, latitude, longitude, and altitude.
 48. Themethod of claim 18 wherein the plurality of sensors comprises atwo-dimensional array of sensors.
 49. The method of claim 48 wherein thetwo-dimensional array of sensors comprises a charge-coupled device (CCD)array.